cold cratonic roots and thermal blankets: how continents ......was proposed by gurnis (gurnis, 1988;...

479

International Geology Review Vol 45 2003 p 479ndash496Copyright copy 2003 by V H Winston amp Son Inc All rights reserved

0020-681403666479-18 $1000

Cold Cratonic Roots and Thermal Blankets How Continents Affect Mantle Convection

VALERY P TRUBITSYN WALTER D MOONEY1

United States Geological Survey 345 Middlefield Rd MS 977 Menlo Park California 94025

AND DALLAS H ABBOTT

Lamont-Doherty Earth Observatory Palisades New York 10964

Abstract

Two-dimensional convection models with moving continents show that continents profoundlyaffect the pattern of mantle convection If the continents are wider than the wavelength of the con-vection cells (~3000 km the thickness of the mantle) they cause neighboring deep mantle thermalupwellings to coalesce into a single focused upwelling This focused upwelling zone will have apotential temperature anomaly of about 200degC much higher than the 100degC temperature anomaly ofupwelling zones generated beneath typical oceanic lithosphere Extensive high-temperature melts(including flood basalts and late potassic granites) will be produced and the excess temperatureanomaly will induce continental uplift (as revealed in sea level changes) and the eventual breakupof the supercontinent The mantle thermal anomaly will persist for several hundred million yearsafter such a breakup In contrast small continental blocks (lt1000 km diameter) do not inducefocused mantle upwelling zones Instead small continental blocks are dragged to mantle down-welling zones where they spend most of their time and will migrate laterally with the downwellingAs a result of sitting over relatively cold mantle (downwellings) small continental blocks are favoredto keep their cratonic roots This may explain the long-term survival of small cratonic blocks (egthe Yilgarn and Pilbara cratons of western Australia and the West African craton) The optimum sizefor long-term stability of a continental block is lt3000 km These results show that continents pro-foundly affect the pattern of mantle convection These effects are illustrated in terms of the timingand history of supercontinent breakup the production of high-temperature melts and sea levelchanges Such two-dimensional calculations can be further refined and tested by three-dimensionalnumerical simulations of mantle convection with moving continental and oceanic plates

Introduction

ARCHEAN CRATONS have thick lithospheric rootsand low heat flow (Grand and Helmberger 1984Pollack et al 1993 Artemevia and Mooney 2001)The preservation of Archean diamonds within theseroots as known from kimberlite eruptions impliesthat they have had low heat flow and thick lithos-phere since they formed ( Richardson et al 1984Boyd et al 1985 Nisbet 1987) Indeed the oldestmodel ages of cratonic roots are indistinguishablefrom the oldest ages of the overlying crust (Pearsonet al 1995) implying that Archean continents haveexperienced low heat flow since they formed

In contradiction to these observations someinvestigators have proposed that continents act asthermal blankets ie low heat conduction through

lithospheric roots causes the underlying asthenos-phere to heat up (eg Anderson 1989) This latterproposal is consistent with the development ofsuperplumes that eventually break up superconti-nents (Condie 1998 White and McKenzie 1995)Late-potassic granites within cratons also implystrong basal heating of the continental lithosphere(Campbell and Hill 1988 Hill et al 1992)Furthermore if we consider Africa today it is sta-tionary with respect to the hot spot reference frameand has an anomalously high topography relative tothe other continents (Cogley 1985) This anomalouselevation is consistent with the thermal blanketmodel the African continental lithosphere is bothheated and uplifted by a deep-seated mantle plume

Thus we seem to have two sets of contradictoryobservations One set implies long-term cold conti-nental roots and a second set implies hot continentalroots In this paper we examine these apparently1Corresponding author email mooneyusgsgov

480 TRUBITSYN ET AL

contradictory observations and show that they canbe reconciled if we allow the thermal history of con-tinental blocks to depend on their lateral size In sodoing we also show the profound affect that conti-nents have on the pattern of mantle convection

Properties of Mantle Convection

Five main properties of convection in the mantleare particularly relevant to this study (1) the exist-ence of cold rigid continental lithosphere underlainby a warm low-viscosity asthenosphere implies theexistence of a large viscosity contrast (gt3000 Pa-s)in the upper mantle (2) regular long-wavelengthconvection in the mantle in combination withhigh-intensity quasi-turbulent convection produceshot regions with varying shapes such as diapirssheets and ridges (3) the olivine-perovskite mantlephase transition at a depth of 660 km is endother-mic and results in partial stratification of convec-tion in the mantle (for example some subductedplates continue to descend into the lower mantlewhereas others remain above the phase transition)(4) mantle material at the typical P-T conditions ofoceanic lithosphere has a viscoplastic rheology thatproduces plate bending and the other mechanicalbehavior that we associate with plate tectonicsand (5) of particular importance to this study thepresence of continents above the convecting mantleprofoundly affects the form of that convection conti-nental ldquothermal blanketsrdquo lead to regular andpredictable patterns in the motions of both theconvection system and the continents

The first three properties were studied in greatdetail during the last three decades (eg see Schu-bert et al 2001) Taking into account the fourthproperty leads to convection models that self-con-sistently describe the breakup of oceanic lithos-phere into quasi-rigid plates (Tackley 2000a2000b Zhong et al 2000) This paper investigatesthe fifth property of mantle convection The effectsof floating continents on mantle convection areimportant on time scales of more than 200 mywhen continents behave like stable rigid bodiesespecially in comparison with the creation and sub-duction of oceanic lithospheric plates

Previous Convection ModelsIncorporating Moving Continents

The role of moving oceanic plates andor conti-nents in mantle convection has been modeled using

a numerical method that actually fixes mantle veloci-ties rather than independently describing plate veloc-ities (Olson and Corcos 1980 Davies 1986 19881989 Gurnis and Hager 1988 Gable et al 1991King et al 1992 Zhong and Gurnis 1995 Doin etal 1997) This approach can explain some aspects ofplate movement but could not be used to calculateplate velocities as an independent parameter

A method for the self-consistent calculation ofcontinental plate velocity within a convecting mantlewas proposed by Gurnis (Gurnis 1988 Gurnis andZhong 1991 Zhong and Gurnis 1993 1994) In thisapproach a continent is considered as a highlyviscous body floating in the mantle Gurnis (1988)calculated the velocity of continents in his 2-Dmodel by using a fixed marker point at the corner ofeach continent This provided the first quantitativedescription of the assembly and dispersal of two con-tinental blocks Additional studies were presentedby Gable et al (1991) Lowman and Jarvis (19931995 1996) Bobrov et al (1999) and Trubitsyn andRykov (1995 1998 2000) The latter authorsapproximated continents as rigid bodies (asdescribed by Eulerrsquos equations of motion) with vis-cous coupling to drive the plates (Trubitsyn 2000)An iterative procedure was used to model convec-tion taking into account the rotation of continentsand their mutual collisions Oceanic plates weredescribed by mantle convection equations incorpo-rating a visco-plastic rheology (Tackley 2000aZhong et al 2000) These studies showed that themantle under a fixed continent will become warmerand that eventually hot upwelling zones arise partic-ularly under large continents However it was shownby Gurnis (1988) Trubitsyn and Rykov (1998) andLowman and Jarvis (1996 1999)mdashand will bedemonstrated heremdashthat the motions of continentsproduce additional effects on mantle evolution

Input Parameters of Convection Models

Due to practical limitations on computationalresources it is not yet possible to make a numericalsimulation of mantle convection that exactlymatches the conditions in the real Earth Ourmodels do not match the real Earth in severalaspects (Table 1) First these models are two dimen-sional while real convection is three dimensionalSecond these models use basal heating onlywhereas both basal and internal heating drive realmantle convection Third our models use muchlower Rayleigh numbers than the Rayleigh number

HOW CONTINENTS AFFECT MANTLE CONVECTION 481

of actual terrestrial convection Due to these limita-tions for simplicity we restrict our conclusions tothose aspects of the modeling that are not stronglydependent on the numerical method used

The Rayleigh number Ra defines the intensityof convection For the present-day mantle it is high(RaE raquo 107) (Schubert et al 2001) Thus mantleconvection is non-steady state and partially chaoticHowever chaotic behavior may obscure the mainpatterns of mantle convection that interest us Toavoid non-steady state effects that occur for highRayleigh numbers (Ra gt 105) we have made simplenumerical models of mantle convection with vari-able viscosity for a Rayleigh number of Raef = 5times104The effects of continents on mantle convectionincrease as the Rayleigh number is decreased soour numerical results emphasize the pure effects ofcontinents and therefore provide simple and clearillustrations for tectonic analysis

Whereas numerical simulations with a lowRayleigh number cannot represent the real Earthsuch simulations illustrate many important proper-ties of convection as noted above Furthermorefully modeling the real Earth presents many techni-cal challenges For example continents movetogether with rigid oceanic plates which haveprofound effects Conrad and Hager (2001) observedthat cold deeply subducting lithosphere stronglyresists plate motion Therefore to model the realEarth at a high Rayleigh number we must alsoinclude the effects of surficial and subductedoceanic plates presently an unsolved problem Thusa numerical model with a low effective Rayleighnumber as presented here is a reasonable compro-mise that even has some advantages over a modelwith high Rayleigh number but no oceanic plates

Our simulations use the viscosity law

h = h0 exp [(ndash46 T + 092(1ndashz)]

where T is dimensionless temperature and z is the ver-tical coordinate Thus viscosity is modeled as temper-ature and pressure dependent Temperature andpressure increases with depth cause viscosity changesof only 2 and 25 orders of magnitude respectively

The system of governing equations and boundaryconditions for these 2-D numerical models are pre-sented in Appendix A We also show results for morerealistic Rayleigh numbers that duplicate the generalfeatures of our low Rayleigh number calculations butwith much greater chaotic behavior in Appendix B

TAB

LE 1

Inp

ut P

aram

eter

s fo

r C

onve

ctio

n M

odel

ing

Syst

emP

rese

nt E

arth

Supe

rcon

tine

ntSm

all c

onti

nent

App

endi

x

Ray

leig

h nu

mbe

r (R

a)1

00E

+07

500

E+

045

00E

+04

20E

6

Hea

ting

Bas

al +

inte

rnal

Bas

al o

nly

Bas

al o

nly

Bas

al +

inte

rnal

Vis

cosi

ty la

wP

ress

ure

tem

pera

ture

and

str

ess

depe

nden

t1

h =

h0e

xp[(ndash

46T

+ 0

92(

1 ndash

z)]

h =

h0e

xp[(ndash

46T

+ 0

92(

1 ndash

z)]

h =

h 0exp

[(ndash4

6T

+ 0

92(

1 ndash

z)]

Con

vect

ion

patte

rnT

hree

-dim

ensi

onal

Two-

dim

ensi

onal

Two-

dim

ensi

onal

Two-

dim

ensi

onal

Con

tinen

t dia

met

er k

mVa

riab

le30

0030

030

00

Sim

ulat

ion

dura

tion

my

38

0034

015

00

500

Pha

se b

ound

ary

at 6

60 k

mYe

sN

oN

oYe

s

Num

ber

of c

ells

Vari

able

105

Vari

able

1 See

for

exa

mpl

e F

orte

and

Mit

rovi

ca 2

000

Sch

uber

t et a

l 2

001

482 TRUBITSYN ET AL

Results Convection with Two Continents that Combine to Form a Supercontinent

Continental assembly

Figure 1 (top) shows a simple 2-D convectionsystem with regularly spaced upwellings (red) anddownwellings (green) Note that the lateral spacingbetween upwellings and downwelling is equal to thedepth of the model here 3000 km (the thickness ofthe mantle) Once mantle convection achieves asteady state we introduce two free-floating conti-nents to the system (Fig 1 t1 = 0 my) The modelinput parameters are listed in Table 1 Our simula-tion starts with each continent on separate upwellingzones separated by a central downwelling zone Thecontinents then begin to move off the upwellingtoward the central downwelling zone (Fig 1 t2 = 4my) At t3 = 15 my (Fig 1C) the two continentalblocks have just combined into a single superconti-nent Each continent moves a distance of ca D4 =750 km over 15 my a mean velocity of 5 cmyr(extrapolated to Ra = 107) The downwelling zonesremain intact and undisturbed until the two conti-nents collide (Fig 1 t3 = 15 my) The two conti-nents are large enough to produce a combinedcontinental block that is wider than the convectioncells (3000 km) Thus for our purposes we define asupercontinent as any continental block with anaverage diameter of over 6000 km

Mantle evolution under a supercontinent

Initially the asthenosphere directly beneath thesupercontinent gets colder (Fig 2 t4 = 80 my) andthus the thickness of the cold thermal boundarylayer beneath the new supercontinent increases Forsimplicity we take the initial temperature distribu-tion in the two continents as being the same as in theoceanic lithosphere and mantle This initial condi-tion lets us show how temperature changes with theaging of the continents The cooling of continentallithosphere and increasing thickness of the thermalboundary layer has been postulated to occur due tocooling by the ongoing subduction of oceanic plateson either side of a supercontinent (Schubert et al2001) However despite this effect we find thedominant factor is the thermal blanketing by thethick low-conductivity continental lithosphereThus the long-term thermal process beneath asupercontinent is the net heating of the mantle

As the mantle beneath the supercontinentwarms it becomes lighter forming a deep low-pres-sure region Because fluids move from regions of

high pressure to regions of low pressure the lowpressure region causes thermal upwelling zones tomigrate in the mantle toward the region beneath thecenter of the supercontinent (Fig 2 t5 = 170 myand t6 = 200 my) The convection cells become nar-rower over time until eventually the three upwellingzones merge into a single giant superplume (Fig 2t6 = 200 my)

The maximum temperature at the center of thesuperplume (Fig 2 t6 = 200 my) is ~200degC higherthan the maximum temperature at the center of anupwelling without continents (Fig 1 t1 = 0 my)Thus large continents result in the production ofmuch hotter plumes

Continental dispersal

After the supercontinent breaks up (Fig 3 t7 =220 my and t8 = 250 my) the area beneath whatwas previously the center of the supercontinentremains hot for several hundred million years (Fig3 t9=290 my and t10 = 340 my) Thus superconti-nents have a long-lasting effect on the temperatureregime within the upper mantle

The state of the suboceanic mantle at t9 = 290my resembles that in the present-day Atlanticwhere the predicted reduced heat flow (ie themantle heat flow) beneath the mid-oceanic region issix times greater than the reduced heat flow beneathcontinents (Gupta 1993) This could explain whymuch of the Mid-Atlantic Ridge is a locus of hotspotvolcanism (Fontigne and Schilling 1996 Yu et al1997 Hanan et al 2000)

Heating of the mantle beneath a supercontinentcan generate dynamic topography Comparing theelevation of the continents during the whole Wilsoncycle as simulated in Figures 1 2 and 3 we see thatcontinents are tilted with one edge standing highfrom ca 50 my before break-up until 50 my afterbreakup Conversely continental elevations are lowwhen the continent sits over a mantle downwellingThus one edge of each continental block should havebeen relatively high for ~100 my before and after thebreakup of Pangea and Rodinia This predictionagrees with low sea level curves (Vail and Mitchum1979 cf discussion by Trubitsyn 2000)2

2We note that an additional opposing factor not consideredhere is the expected rise in sea level during supercontinentbreakup due to creation of a larger volume of oceanic spread-ing ridges


Figure 4 shows continental velocities during theWilson cycle Note that we do not know exactly howlong it takes for two colliding continents to mergeinto a supercontinent Also our model does notinclude a calculation of the critical stresses that are

required to break up a supercontinent Figure 4shows that their relative velocities are two times lessthan the typical mantle convection velocity of 10cmyr Continental velocity is nearly zero during twotime periods t = 15ndash200 and t gt 340 my

FIG 1 Three time steps (0 4 and 15 my) illustrating the influence of two continents on the convecting mantleModel parameters are from Table 1 governing equations are from Appendix A Colors depict dimensionless subadiabatic(potential) temperature from 1 to 0 Length of arrows is proportional to mantle velocities The longest arrows equal amantle velocity of roughly 10 cmy The red line above each picture shows the calculated distribution of surface dimen-sionless heat flow ie the Nusselt number Nu (x) The time of each simulation in my is shown on the right side At 0my two continents are instantaneously placed in the steady-state convecting mantle At 4 my the continents havemoved away from the pink upwellings and approach each other above a green downwelling At 15 my the continentshave formed a ldquosupercontinentrdquo where previously a cold downwelling existed Note that the supercontinent (15 my) hasdisturbed the initial steady-state convection (0 my)

484 TRUBITSYN ET AL

Convection with a Small Continent

In this numerical simulation (Figure 5 Table 1)each convection cell has nearly the same width andthe same height and there are few changes withtime Next we introduce a small free-floating conti-nent into the system (Fig 5 t1 = 0 my) The conti-

nent is just 300 km wide (01 of the mantle depth)The thickness of the continental block is 005 of thethickness of mantle ie 150 km At the start of oursimulation the continent is between an upwellingand a downwelling zone The continent moves fromthe upwelling zone toward a downwelling (Fig 5 t2 =50 my) During this time the continent has moved

FIG 2 Further evolution of the convection system in Figure 1 The green line above each picture is the topography(in km) of the surface of the model At 80 my the supercontinent is depressed by the last vestiges of the downwellingAt 170 my two small upwellings (brown) begin to migrate to the center of the supercontinent At 200 my these upwell-ings have merged and the supercontinent has positive topography At 220 my the initial rifting of the supercontinenthas begun due to vigorous upwelling beneath the supercontinent


about 1000 km Thus its mean velocity is 2 cmyrless than half the mantle velocity

Once this small continent arrives at the down-welling zone it remains there for most of the remain-ing time At t3 = 200 my (Fig 5) the continent hasalready spent 150 my at the downwelling Thepresence of the continent only produces a small

change in the left-hand upwelling generating a fea-ture that looks like a small plume Further calcula-tion shows that this plume has an insignificant effecton the continent Only after about 1 Gy (Fig 5) doupwellings begin to move along the base of themodel to a position beneath the continent Furthercalculation shows that these upwellings are not large

FIG 3 Further evolution of the convection system in Figures 1 and 2 These three diagrams document the stages ofcontinental dispersal At 250 my the continents continue to move apart and have uplifted rift shoulders much like theregion bordering the present-day Red Sea At 290 my the continents have moved far apart but the superplume contin-ues to be active where the supercontinent had been (x = 50) The far edges of the continents have encountered down-wellings and are tilted in sympathy At 340 my the continents are far apart and sit above strong downwellings wherethey are depressed by 200ndash300 m

486 TRUBITSYN ET AL

enough to push the continent away from the down-welling Thus a downwelling essentially traps smallcontinents in place (Fig 5 t1 = 0 yr t5 = 15 Gy)

Mantle convection in the real Earth which has alarger Rayleigh number is nonsteady and chaotic(Schubert et al 2001) As a result the convectioncells change their size over time Therefore evena small continent caught by a downwelling will notbe fixed in space It will migrate along with thedownwelling

In the case where many small continents arepresent (as would be true for most if not all of theEarthrsquos history) there can be additional effectsEach small continent quickly (in ca 10ndash50 my)moves to a downwelling If the number of continentsis greater than the number of downwellings two orthree small continents go to one downwelling col-lide and coalesce to form a larger continent Whenthe lateral extent of this larger continent is compara-ble to the width of the convection cells (~3000 km)the supercontinent begins to act as a thermalblanket to convection and is able to leave thedownwelling

A continent with a diameter close to the mantlethickness (3000 km) spends roughly one-third of itstime on a downwelling one-third of its time as a partof a supercontinent on an upwelling and one-thirdof its time moving between downwellings and

upwellings Our model shows that without addi-tional external forcing a small continent with adiameter of about 300 km cannot leave its down-welling for at least 1 Gy This cold state of a smallcontinent (in parallel with buoyancy and rheology)prevents continental lithosphere from mixing intothe mantle and preserves lithospheric roots

Discussion Geological Implicationsof Modeling Results

In both numerical simulations presented herecontinents produce significant changes in the mor-phology of upwelling and downwelling zones Down-welling zones deviate from their former verticalgeometry when continents approach and partiallycover them This suction effect of continents on sub-duction zones has been noted before (eg Uyeda1982) and results in the familiar dipping subduc-tion zone This is well defined by deep seismicityand seismic tomography

Likewise upwelling zones that move beneathcontinents also lose their highly regular geometryand become much wider near their tops When asupercontinent is present the upper parts of theupwelling zones form the classic bulbous shape thatwas produced experimentally by Campbell and Grif-fiths (1989) This geometry of plume heads is

FIG 4 Calculated velocities for both continents (v cmy) after extrapolation to Ra = 107 A solid line is used torepresent continent 1 and a dashed line continent 2 The cycle from supercontinent formation to full dispersal requires300 my


confined to supercontinents and does not occurbeneath a small continent The interior of the plumehead has the highest temperatures and is the mostlikely source for high-T komatiitic lavas

These 2-D numerical models are consistent withearlier suggestions that continents can act as ther-mal blankets However effective thermal blanketingis a function of continental size We estimate the

FIG 5 Evolution of mantle convection with the presence of a small continent (length l = 300 km thickness d = 150km) and for Raef = 5 times 105 in an elongated box with five convection cells The colors depict dimensionless subadiabatic(potential) temperature from 1 to 0 Length of arrows is proportional to mantle velocities The longest arrows equal amantle velocity of ca 7 cmy (after extrapolation to Ra = 107) At 0 my the continent moves to the right away from theupwelling (pink) At 200 my the continent is caught by the downwelling (green) From 200 my to 15 Gy the continentremains with the downwelling but the convection system continues to evolve and does not reach steady state Thus evena small continent affects the pattern of convection

488 TRUBITSYN ET AL

threshold size to be equal to the thickness of themantle (3000 km) When we compare this thresholdsize to the size of cratonic blocks we see that theaverage diameter of the largest preserved cratonicblocks is 1500 to 3350 km (Table 2) Only oneArchean cratonic block that of North America hasa diameter larger than 3000 km The maximumdiameter of the Archean of North America (3356km) is very similar to our estimated threshold diam-eter (3000 km) of non-supercontinental cratonicblocks Larger cratonic blocks are more likely to berifted and thus reduced in size

Several continents (ie including portionsyounger than the Archean) have diameters sup33000

km (Table 3) We note that all but one of the conti-nental blocks with diameters exceeding 3100 km(Table 3) contain one or more Cenozoic continentalrifts North America contains the Basin and RangeProvince Antarctica has the East Antarctic riftzone Africa is cut by the East African rift zone andEurasia which has a radius of more than twice 3000km has two prominent Cenozoic riftsmdashthe Baikalrift and the extensive Western European rift systemOnly South America appears to violate this precept(the Amazon rift and the rift-related Parana basinare pre-Cenozoic and are not considered here)However the geometry of South America is elon-gated north to south such that it may fit above a

TABLE 2 Diameter Calculated for Circular Archean Cratonic Blocks as Amalgamated by 16-18 Gy1

Archean core Surface area km2 Diameter km

North America 885E + 06 335605

East Antarctica 581E + 06 271890

Kaapvaal-Rhodesia 145E + 06 1358608

Pilbara + Yilgarn 151E + 06 1384968

East European Platform 188E + 06 1545303

Siberia 372E + 06 2175623

India 196E + 06 158094

Central Africa 58E6 2723863

Amazon 134E6 1306925

1Data from Abbott and Menke 1990 Stoddard and Abbott 1996

TABLE 3 Diameter Calculated for Circular Continental Blocks1

Continent Surface area km2 Diameter km


Antarctica 107E + 07 3688

Arabia 397E + 06 2247

Australia 749E + 06 3088

Eurasia 391E + 07 7052

India 431E + 06 2342

Africa 215E + 07 5233

South America 110E + 07 3740

1Data from Stoddard and Abbott 1996


single convection cell In contrast to the examplescited above none of the three smaller continentalblocks (average radius lt3100 km) has an internal rift

Inasmuch as modeling suggests that a supercon-tinent sweeps together the mantle convection cellsbeneath this implies that the magnitude of the tem-perature anomaly beneath a supercontinent is afunction of its average diameter The biggest super-continents should produce the largest thermalanomalies and the highest degrees of partial meltsThis inference seems to be borne out in the case ofPangea which produced the largest known floodbasalt province (Abbott and Isley 2002) and is thelargest known supercontinental block of thePhanerozoic (Marzoli et al 1999)

These models suggest that the hottest mantlemelts are preferentially produced beneath super-continents and rifted oceanic basins formed duringtheir breakup The widest feeder dikes are producedby the largest plumes and field evidence from suchdikes suggest that there were many Precambriansupercontinents the size of Pangea or larger Abbottand Isley (2002) estimated that there were six plumeevents in the Archean and Early Proterozoic each atleast 10 times as large as the Pangean superplumeAlthough a few of these plume events have a geo-chronology that might be coincident there were atleast four separate plume events 10 times as large asthe Pangean superplume Could each of these fourmassive plume events represent the legacy of asupercontinent that was significantly larger thanPangea A combination of precise geochronologyand paleomagnetic data will be required to testthese ideas

Late potassic granites are postulated to form asthe result of a long-lived (100 my) thermal anomalyin the underlying mantle (Campbell and Hill 1988)The long residence times of supercontinents overdownwellings suggests that such potassic graniteswere formed when that continent was part of asupercontinent This hypothesis is consistent withanother observation that late potassic granitesalmost invariably follow a period of consolidation ofsmaller cratonic blocks into a larger cratonic blockLate potassic granites tend to be a mark of craton-ization in that the craton tends to undergo no signif-icant internal deformation after this event

If late potassic granites do reflect widespreadheating of the base of the cratonic lithosphere by asupercontinent-induced plume they may also bemarkers for another event The mechanism for theformation of cratonic roots is still debated but it is

agreed that cratonic roots are very refractory andrigid It has been suggested that recent continentalsuperplume events have resulted in the addition ofmaterial to the base of the craton in South America(VanDecar et al 1995) If this also occurred duringthe Archean some cratonic roots may be composedof refractory mantle residues resulting from theextraction of superhot plume lavas during a super-continental epoch This model can be tested bylooking at the degree of stratification by Mg numberof cratonic roots in areas with late potassic granitesIt can also be tested by comparing the ages of thesestratified roots to the ages of the potassic granitesBecause the thermal pulse will take a long time totravel through the lithosphere to the base of thecrust the base of the cratonic root should be tens ofmillions of years older than the age of the late potas-sic granites (Campbell and Hill 1988 Hill et al1992) The base of the cratonic root should also havethe same age as the region intruded by the latepotassic granites

Conclusions

We used very simple 2-D numerical simulationswith low Rayleigh numbers to reveal the affects ofcontinents on mantle convection These models donot take into account non-steady state nor sphericaleffects as described by Schubert et al (2001) How-ever the models illustrate important qualitativeeffects and provide a guide for interpretingobserved geological data These simulations showthat mantle convection is significantly affected bydrifting continents Large continents (gt3000 km indiameter) are highly effective as thermal blanketsand cause the underlying mantle to heat up Thisthermal blanketing produces a low-pressure zonewithin the mantle that sweeps together thermalupwellings beneath the continent into a superplumeAs a result supercontinents generate the forces fortheir own dispersal by rifting Large (~1 km)dynamic topography is also produced by hot buoy-ant mantle upwellings as are extensive high-tem-perature mantle melts

Smaller continents (lt1000 km in diameter) aretoo small to sweep up thermal convection cellsInstead smaller continents tend to migrate towarddownwelling zones and to remain there Smallercontinents develop thermal boundary layers that aretoo thick to be thermally eroded when the block isover an upwelling zone

490 TRUBITSYN ET AL

Many factors prevent mixing of the cratoniclithosphere into the mantle (Lenardic and Kaula1995 Lenardic 1997 1998 Moresi and Lenardic1997) They are as follows high viscosity chemicalbuoyancy and viscoplastic rheology We have onlystudied the evolution of the thermal state of floatingcontinents not the evolution of their buoyancy andrheology Because the viscous forces of mantle flowtend to permanently drag smaller continents to thecoldest downwellings a small continent spendsmost of its time in a relatively cold state Thereforethe viscosity of continental roots of small cratonsremains relatively high

Our results and those of previous papers (Gurnis1988 Gurnis and Zhong 1991 Zhong and Gurnis1993 1994 Trubi tsyn and Rykov 19951998 2000 Bobrov et al 1999 Lowman andJarvis 1966 1999 Trubitsyn 2000) indicate thatthe mantle-continent convection system has twoquasi-steady states during which continents aremotionless In the first state the continents areassembled into a supercontinent and in the secondstate each continent occupies its own downwellingDuring the Earthrsquos history the mantle-continent sys-tem has oscillated between these two states Onaverage the continents assemble and disperse every500ndash800 Ma

Continents also affect the shape of mantleupwelling and downwelling zones Beneath super-continents the shape of an upwelling zone justbefore continental breakup resembles the classicbulbous shape that is attributed to plume headsDownwelling zones deviate from the vertical andbecome more narrow at the edge of continents andare sucked beneath the continent by the low-pres-sure zone that they generate Thus the low subduc-tion angles of some Benioff zones are partly due tothe presence of continental blocks

Continents play a major role in influencing thepattern of convection in the Earth These simplesimulations illustrate in two dimensions some of theimportant aspects of this role Likewise changes inmantle convection can induce the uplift rifting anddispersal of a supercontinent as well as generatehigh-temperature melts all processes that arepreserved in the geologic record

We do not present a model of convection in thereal Earth The main defects of our model are that(1) a 2-D Cartesian model cannot describe cylindri-cal plumes (2) use of a low Rayleigh number in themodel suppresses secondary convection beneathplates effects that were considered by Solomatov

and Moresi (2000) and (3) the effects of highlyviscous oceanic lithosphere which are very impor-tant for mantle convection are not includedExtending these numerical simulations to threedimensions increasing the Rayleigh number andincluding the effects of oceanic lithosphere holdsthe promise of providing a deeper understanding ofthe interplay between mantle convection and theevolution of the continents

Acknowledgments

George A Thompson has long provoked andinspired thoughts regarding the processes that drivethe evolution of continents We thank him for hisstimulating discussions over the past many years VRykov assisted in the development of the numericalcodes used here Numerous people focused ourthinking and reviews of an early version of thispaper by I M Artemieva G S Chulick K CCondie S Detweiler W B Hamilton M KrasnovaS Murphy and N Sleep are greatly appreciatedOur thanks to Gary Ernst and Simon Klemperer fororganizing an outstanding symposium where theseand other ideas were debated

REFERENCES

Abbott D H and Isley A E 2002 The intensity occur-rence and duration of superplume events and erasover geological time Journal of Geodynamics v 34 p365ndash387

Abbott D H and Menke W H 1990 The length of theglobal plate boundary at 24 Ga Geology v 18 p 58ndash65

Anderson D L 1989 Theory of the Earth Boston MABlackwell Scientific Publishers 366 p

Artemieva I M and Mooney W D 2001 Thermalthickness and evolution of Precambrian lithosphere Aglobal study Journal of Geophysical Research v 106p 16387ndash16414

Blankenbach B Busse F Christensen U Czerepes LGunkel D Hansen U Jarvis G Koch M Mar-quatt G Moore D Olson P Schmeling H andSchnaubelt T 1989 A benchmark comparison forconvection codes Geophysical Journal Internationalv 98 p 23ndash38

Bobrov A M Jacoby W and Trubitsyn V P 1999Effects of Rayleigh number length and thickness ofcontinent on time of mantle flow reversal Journal ofGeodynamics 27 133ndash145

Boyd F R Gurney J J and Richardson S H 1985Evidence for a 150-200-km thick Archean lithosphere


from diamond inclusion thermobarometry Nature v315 p 387ndash409

Campbell I H and Griffiths R W 1990 Implication ofmantle plume structure for the evolution of fluidbasalts Earth and Planetary Science Letters v 99 p79ndash93

Campbell I H and Hill R I 1988 A two-stage modelfor the formation of the granite-greenstone terrains ofthe Kalgoorlie-Norseman area Western AustraliaEarth and Planetary Science Letters v 90 p 11ndash25

Cogley JG 1985 Hypsometry of the continentsZietschrift fuumlr Geomorphologie Supplementband 53

Condie K C 1998 Episodic continental growth andsupercontinents A mantle avalanche connectionEarth and Planetary Science Letters v 163 p 97ndash108

Conrad C P and Hager B H 2001 Mantle convectionwith strong subduction zones Geophysical JournalInternational v 144 p 271ndash288

Davies D G 1986 Mantle convection under simulatedplates Effects of heating modes and ridge and trenchmigration and implication for core-mantle boundarybathymetry geoid and Benioff zone Journal of theRoyal Astronomical Society v 84 p 153ndash183

______ 1988 Role of the lithosphere in mantle convec-tion Journal of Geophysical Research v 93 p10451ndash10466

______ 1989 Mantle convection model with a dynamicplate Topography heat flow and gravity anomaliesGeophysical Journal International v 98 p 461ndash464

Doin M-P Fleitout L and Christensen U 1997 Man-tle convection and stability of depleted and undepletedcontinental lithosphere Journal of GeophysicalResearch v 102 p 2771ndash2787

Fontigne D and Schilling J G 1996 Mantle heteroge-neities beneath the South Atlantic a Nd-Sr-Pb isoto-pic study along the Mid-Atlantic Ridge (3degndash46deg S)Earth and Planetary Science Letters v 142 p 209ndash221

Forte A M and Mitrovica J X 2001 Deep-mantlehigh-viscous flow and thermochemical structureinferred from seismic and geodynamic data Nature v410 p 1049ndash1056

Gable C W OrsquoConnell R J and Travis B J 1991Convection in three dimensions with surface platesGeneration of toroidal flow Journal of GeophysicalResearch v 96 p 8391ndash8405

Grand S P and Helmberger D V 1984 Upper mantlestructure beneath of North America Geophysical Jour-nal of the Royal Astronomical Society v 76 p 399ndash438

Gupta M L 1993 Is the Indian Shield hotter than otherGondwana shields Earth and Planetary Science Let-ters v 115 p 275ndash285

Gurnis M 1988 Large-scale mantle convection andaggregation and dispersal of supercontinents Naturev 332 p 696ndash699

Gurnis M and Hager B H 1988 Control of the struc-ture of subducted slab Nature v 335 p 317ndash321

Gurnis M and Zhong S 1991 Generation of long wave-length heterogeneities in mantle dynamics Interactionbetween plates and convection Geophysical ResearchLetters v 18 p 581ndash584

Hanan B B Blichert-Toft J Kingsley R and SchillingJ G 2000 Deplated Iceland mantle plume geochem-ical signature Artifact of multicomponent mixingGeochemistry Geophysics and Geosystems 1-2000American Geophysical Union and the GeochemicalS o c i e ty U ni t e d S ta t es [ pa p er n um b e r1999GC000009]

Hill R I Campbell I H Davies G F and GriffithsR W 1992 Mantle plumes and continental tectonicsScience v 256 p 186ndash193

King S D Gable C W and Weinstein S A 1992Model of convection-driven tectonic plate A compari-son of methods and results Geophysical Journal Inter-national v 109 p 481ndash487

Lenardic A 1997 On the heat flow variation fromArchean cratons to Proterozoic mobile belts Journal ofGeophysical Research v 102 p 709ndash721

______ 1998 On the partitioning of mantle heat lossbelow oceans and continents over time and its relation-ship to the Archean paradox Geophysical JournalInternational v 134 p 706ndash720

Lenardic A and Kaula W M 1995 Mantle dynamicsand the heatflow into the Earthrsquos continents Nature v378 p 709ndash711

Lowman J P and Jarvis J T 1993 Mantle convectionflow reversal due to continental collisions Geophysi-cal Research Letters v 20 p 2087ndash2090

______ 1995 Mantle convection models of continentalcollision and breakup incorporating finite thicknessplates Physics of the Earth and Planetary Interiors v88 p 53ndash68

______ 1996 Continental collisions in wide aspect ratioand high Rayleigh number Two-dimensional mantleconvection models Journal of Geophysical Researchv 101 p 25485ndash25497

______ 1999 Effects of mantle heat source distributionon supercontinent stability Journal of GeophysicalResearch v 104 p 12733ndash12746

Marzoli A Renne P R Piccirillo E M Ernesto MBellieni G and De Min A 1999 Extensive 200-mil-lion-year-old continental flood basalts of the CentralAtlantic Magmatic Province Science v 284 p 616ndash618

Moresi L-N and Lenardic A 1997 Three-dimensionalnumerical simulation of crustal deformation and sub-continental mantle convection Earth and PlanetaryScience Letters v 150 p 223ndash243

Nisbet E G 1987 The young Earth An introduction toArchean geology Boston MA Allen and Unwin402 p

492 TRUBITSYN ET AL

Olson P and Corcos G M 1980 Boundary layer modelfor mantle convection with surface plates GeophysicalJournal of the Royal Astronomical Society v 62 p195ndash219

Pearson D G Shirey S B Carlson R W Boyd F RPokhilenko N P and Shimuzu N 1995 Re-OsSm-Nd and Rb-Sr isotopic evidence for thick Archeanlithospheric mantle beneath the Siberian craton modi-fied by multistage metasomatism Geochimica et Cos-mochimica Acta v 59 p 959ndash977

Pollack H N Hurter S J and Johnson J R 1993Heat flow from the Earthrsquos interior Analysis of the glo-bal data set Reviews of Geophysics v 31 p 267ndash280

Richardson S H Gurney J J Erlank A J and HarrisJ W 1984 Origin of diamonds in old enriched man-tle Nature v 310 p 198ndash202

Samarskii A A and Nikolaev E S Methods offinite-difference equations solving Moscow NaukaPress 1978 591 p (in Russian)

Schubert G Turcotte D L and Olson P 2001 Mantleconvection in the Earth and planets Cambridge UKCambridge University Press 940 p

Solomatov V S and Moresi L-N 2000 Scaling oftime-dependent stagnant lid convection Applicationto small-scale convection on Earth and other terrestrialplanets Journal of Geophysical Research v 105 p21795ndash321817

Stoddard P R and Abbott D H 1996 The influence ofthe tectosphere upon plate motion Journal of Geo-physical Research v 101 p 5425ndash5433

Tackley P J 2000a Self-consistent generation of tectonicplates in time-dependant three-dimensional mantleconvection simulations 1 Pseudoplastic yieldingGeochemistry Geophysics and Geosystems v 1[paper number 2000G000036]

______ 2000b Self-consistent generation of tectonicplates in time-dependent three-dimensional mantleconvection simulations 2 Strain weakening andasthenosphere Geochemistry Geophysics and Geo-systems v 1 [paper number 2000GC000043]

Trubitsyn V P 2000 Principles of the tectonics of float-ing continents Izvestiya Physics of the Solid Earth v36 p 101ndash113

Trubitsyn V P and Rykov V V 1995 A 3-D numericalmodel of the Wilson cycle Journal of Geodynamics v20 p 63ndash75

_______ 1998 A se l f -c onsi s ten t 2D mode l o fmant le convection with a f loating continent

Russian Journal of Earth Sciences v 1 p 1ndash10[httpwwwaguorgwpsrjes]

______ 2000 3-D spherical models of mantle convectionwith floating continents US Geological Survey OpenFile Report 00-218 44 p

Trubitsyn V P Rykov V V and Jacoby W 1999 Aself-consistent 2-D model for the dip angle of mantledownflow beneath an overriding continent Journal ofGeodynamics v 28 p 215ndash224

Uyeda S 1982 Subduction zones An introduction tocomparative subductology Tectonophysics v 81 p133ndash159

Vail R M and Mitchem R M 1979 Global cycles ofthe relative changes of the sea level from seismicstratigraphy in Watkins J S Montadert L andDickerson P W eds Geological and geophysicalinvestigations of continental margins American Asso-ciation of Petroleum Geologists Memoir 29 Tulsa OK

VanDecar J C James D E and Assumpcao M 1995Seismic evidence for a fossil mantle plume beneathSouth America and implications for plate drivingforces Nature v 378 p 25ndash31

White R S and McKenzie D 1995 Mantle plumes andflood basalts Journal of Geophysical Research v 100p 17543ndash17585

Yu Dongmei Fontigne D and Schilling J G 1997Mantle-plume interactions in the central North Atlan-tic a Nd isotope study of Mid-Atlantic Ridge basaltsfrom 30 degrees N to 50 degrees N Earth and Plane-tary Science Letters v 146 p 259ndash272

Zalesak ST 1979 Fully multidimensional flux-cor-rected transport algorithms for fluids Journal of Com-puters and Physics v 31 p 335ndash361

Zhong S and Gurnis M 1993 Dynamic feedbackbetween a continent-like raft and thermal convectionJournal of Geophysical Research v 98 p 12219ndash12232

______ 1994 Role of plates and temperature-dependentviscosity in phase change dynamics Journal of Geo-physical Research v 99 p 15903ndash15917

______ 1995 Mantle convection with plates and mobilefaulted plate margins Science v 267 p 838ndash843

Zhong S Zuber M T Moresi L and Gurnis M 2000Role of temperature-dependent viscosity and surfaceplates in spherical shell models of mantle convectionJournal of Geophysical Research v 105 p 11063ndash11082


Appendix A

System of governing equations

Convection with moving rigid continents isdescribed using the classical equations of mantleconvection and Eulerrsquos equations for the motion of abody The mantle is modeled by a liquid with vari-able viscosity and a phase transition The rigid con-tinent is assumed to be submerged in the convectionmantle like an iceberg in the ocean Viscous drag ofthe convecting mantle moves the floating continentThe boundary conditions applied to the surfacessubmerged in the mantle take into account all ther-mal and mechanical interactions with the viscousmantle We are therefore able to compute both thevelocity and heat flux of the continent Our numeri-cal code for mantle convection was verified by abenchmark comparison (Blankenbach et al 1989)In order to assess numerical stability we have com-pared results obtained with various grid spacingsand Rayleigh numbers

Equations of mantle convection

Thermal convection in a 2-D model is classicallydescribed by the Stokes equation the equations ofheat transfer and the equation of continuity withvariable parameters (cf Schubert et al 2001)

ndashparapparax +para[h(paraVxparaz + paraVzparax)]paraz +

2para(hparaVxparax)parax = 0 (1)

ndashparapparaz +para[h(paraVzparax + paraVxparaz)]parax +

2para(hparaVzparaz)paraz + Ra0 aT= 0 (2)

paraTparat +VxparaTparax + VzparaTparaz =

(paraparax)(parakTparax) + (paraparaz)(parakTparaz) + H (3)

paraVxparax + paraVzparaz = 0 (4)

where Vx and Vz p and T are dimensionless compo-nents of velocity pressure and temperature respec-tively and H is the internal heat production As iscustomary equaitons 1-4 are given in dimensionlessform with the following parameters D for distancek0 for the thermal conductivity k0 = k0rcp for thethermal diffusivity h0 for the viscosity k0D for thevelocity T0 for the temperature D2k0 for the timeh0k0D2 for the stresses a0 for the coefficient ofthermal expansion and cp0 for the thermal capacityThe Rayleigh number

Ra= a0rgT0 D3 (k0 h0)

controls the intensity of mantle convection where gis the acceleration due to gravity and r is the den-sity Equations 1ndash3 can also be used to describemantle phase transitions if we use generalized effec-tive parameters a cp and compressibility 1Kwhich include phase transitions with delta functionsfor the phase distribution (Schubert et al 2001)

Equations of motion for the continents

We assume a continent to be a thick perfectlyrigid plate In a 2-D model the velocities of allpoints of the continents u (ux uz) are equal to thevelocity of the center of gravity for the plate ux (xz) =u0 uz (xz) = 0

A continent is propelled by the viscous forces ofthe mantle flow The equation for its horizontalmotion takes the form (Trubitsyn and Rykov 1995Trubitsyn et al 1999)

(5)

where m is the dimensionless mass of the continen-tal plate per unit length in the y-direction d and lare the thickness and length of the continent andx1(t) and x2(t) = x1(t) + l are the instantaneousco-ordinates of its left and right edges respectivelysatisfying the condition

dx1 dt = u0 (6)

For slow convection in the mantle the accelera-tion of a continent is very small and its motion issimilar to mantle flow The relation of the left side ofeq (5) to the right side is of order krh0 ~ 10ndash23Therefore the right side of eq (5) can be set equalto zero and the equation of motion of the continentis reduced to an integrated condition of forcebalances

mparau0 parat

p( )x x1= 2h para( Vx parax )x x1=ndash[ ] z


h paraVx paraz( )z 1 dndash=

paraVz paraz( )z 1ndash d=

+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL

The equation for the temperature Tc (x z) withinthe continent in the basic co-ordinate systemincludes the advective temperature with the velocityof the continent u0 along the axis x

paraTcparat + u0paraTcparax =

(parakcparax)(paraTcparax) + (parakcparaz)(paraTcparaz) + Hc (7)

where k0 is the thermal diffusivity for a continentand Hc is its thermometric radioactive internal heatproduction

Boundary conditions

We assume continuity for the temperature andthe heat flow and a no-slip boundary for the velocityVx = u0 and Vz = 0 on the submerged bottom andsides of the continent As a result eq 5 may be sim-plified (Trubitsyn et al 1999) to

(8)

Thus the unknowns to be found in the mantle arethe velocity components Vx(xz) and Vz(xz) pres-sure p(xz) and temperature T(xz) Other unknownvariables to be solved for are the velocity u0(x) at thecenter of the rigid plate the temperature within thecontinent Tc(xz) and the co-ordinate of its left edgex1(t) These seven unknown variables are found fromthe four equations of convection (1ndash4) coupled withthe three equations of a moving plate (6ndash8) As theseequations contain the large square-law terms VxparaTparax VzparaTparaz and u0paraTcparax the system of the equa-tions of mantle-continent is strongly nonlinear

The set of equations (1ndash8) is solved by afinite-difference method based on flux-correctedtransport algorithms (Zalesak 1979) for tempera-

ture transfer and alternating triangular matrixdecomposition with iterative parameters obtained bythe conjugate gradient method for velocities andpressure (Samarskiy and Nikolayev 1978)

Calculation of elapsed time in numerical model

In order to partially remove the bias that is asso-ciated with a lower Rayleigh number we have runour models for a long period of geological time Wehave calculated the model time by extrapolating thecalculated value of variables to Ra raquo 107 TheNusselt number Nu defines efficiency of heattransfer and is the ratio of total heat flux to pureconductive heat flux According to the boundarylayer theory of mantle convection (Schubert et al2001) mantle velocity V is proportional to Ra23 andNu~Ra13 Therefore the typical time for masstransfer tv is proportional to Randash23 The typicaltime for heat transfer tq can be found from adimensional analysis for equations of heat transferand Nusselt number Let us change all differentialsin the equations paraTparat = kpara2Tpara z2 ndash Vz paraTparaz andNu = (VzT ndash kparaTparaz)(kDTD) using finite differ-ences Ttq = kTD2 ndash VzTD and Nu = (VzT ndash kTD)(kTD)

By eliminating Vz we find tq = D2(k Nu) As aresult we have tv ~ Randash23 and tq~ Randash13 or on aver-age t~ Randash12 Therefore to extrapolate the data cal-culated for Ra = 5 times 104 to the real Earth with Ra =107 we need to use these extrapolated units for timet = D2k0 (RaRaE)ndash12 = 3 times 1011 y times (1075 times 104)ndash12

raquo 20Besides horizontal motion of the continents we

also illustrate their uplift by hot buoyant upwell-ings Such dynamic topography of the free surfacewhich is in equilibrium with the convecting mantlemay be calculated using the relation

h = (p ndash 2 hparaVparaz)rg

The maximum geoid anomaly is less than 100 m andthe relief anomaly is on the order of 1 km

Appendix B

The results presented in Figures 1ndash5 were calcu-lated for a low Rayleigh number (Ra = 2 times 104) inorder to avoid the non-steady state and partiallychaotic convection that occurs for higher Rayleighnumbers To illustrate the effect of using a higherRayleigh number (Ra) we present a numerical sim-ulation for a moving continent of size 3000 km and

Raef = 2 times 106 including effects of a phase boundaryat a depth of 660 km and internal heating

The blanketing effect of a stationary continentcan reverse mantle flow from convective down-welling to upwelling in the time period t~100-300my However if the continent moves at a velocitygreater than Dt = 3 times 108 cm108 yr = 3 cmyr where

p( )x x1 l+= p( )x x1=ndash[ ] zd

1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=


D is the thickness of the mantle the mantle hasinsufficient time to heat up and there is no blanket-ing effect We demonstrate this important observa-tion with a model of mantle convection with a

superadiabatic Rayleigh number Raef = 2 times 106 andinternal heating H = 20 (which corresponds abouthalf heating from below and half inside) Also wetake into account the phase transition at 660 km

FIG B1 Evolution of mantle convection with the presence of a single large continent (l = 3000 km) and for Raef = 2 times106 The model is both basally and internally heated and includes a phase boundary at 660 km Note that the convectionpattern is much more chaotic than in Figures 1ndash5 The color scale for dimensionless temperature is the same as that usedin Figure 1 At times t1= 0 and t2 = 40 my the continent is free floating At times t3 = 200 my and t4 = 500 my thecontinent is restrained from moving As expected the continent moves away from the strong upwelling at x = 31 How-ever due to the higher Rayleigh number and more complex convection pattern it is more difficult to isolate thelong-wavelength effect of the continent on the system For this reason we have used a lower Rayleigh number in thesimulations of Figures 1ndash5

496 TRUBITSYN ET AL

which is the most significant phase transition formantle convection The Claperon slope of the phasetransition was taken as g1 = dpdT = ndash2 MPaK anda density jump of Drr = 009 was assumed at thephase transition

The calculations were done for an elongated 2-Dbox with an aspect ratio of 51 and with a grid of 400 times150 and 400 times 300 which corresponds to spacesteps Dx = 00125 = 375 km and Dz = 000667 = 20km or 10 km respectively The dimensionless vis-cosity was taken as a function of the super-adiabatictemperature and hydrostatic pressure in the formh(T p) = 50 times exp [ndash69 T + 46(1 ndash z)]

Due to the temperature increase from the top tothe bottom of the mantle viscosity decreases bythree orders of magnitude However the pressurechange between the top and bottom of the mantleincreases viscosity by two orders of magnitude Themean logarithm of dimensionless viscosity is equalto about 1 The thickness of the continent was takenas d = 00333 = 100 km and the length as l = 09 =2700 km

Figure B1 (t = 0 my) shows the state of mantleconvection at the exact moment when the continentwas instantaneously introduced into the mantleNote that the mantle convection is non-steady stateDownwellings (green) and upwellings (pink) pene-trate through the phase boundary but often changetheir form as they pass through the boundary Forexample a downwelling at x = 07 splits at the phaseboundary and a downwelling at x = 37 becomeswider at the phase boundary The upwelling at x =

12 bends to the left and the upwelling at x = 32branches horizontally before reaching the phaseboundary at z = 05 Due to viscous drag the conti-nent moves to the left At t = 40 my it has moved Dx raquo400 km with a mean velocity V raquo 1 cmy This veloc-ity is about 5ndash7 times less than the mantle velocityIt can be explained by the hindering effect of thesubduction zone in front of the continent The simu-lation at t = 40 my shows the situation when the leftcorner of the continent encounters a downwellingand disturbs the geometry of the uppermost limb ofthis downwelling As a result the downwellingslopes under the continent much like a subductingplate This stage of the mantle-continent systemmimics the present state of the South American con-tinent The blanketing effect has not yet appeared

At time t = 200 my the continent has slowlymoved further to the left and we have stopped thecontinent from moving This lack of motion inducesthe blanketing effect and the mantle under the con-tinent becomes warmer As a result the pressure inthe mantle under the continent becomes lower Thelow pressure is sufficient to pull upwellings alongthe core-mantle boundary At time t = 500 my thestrong upwelling that was at x = 30 at time t = 200my has shifted to x = 20 and an additional weakerupwelling has appeared at x = 26

This simulation emphasizes the more chaoticconvection for higher Rayleigh numbers and illus-trates the blanketing effect of a near-motionless con-tinent such as present-day Africa See alsoTrubitsyn and Rykov (1998)

480 TRUBITSYN ET AL

contradictory observations and show that they canbe reconciled if we allow the thermal history of con-tinental blocks to depend on their lateral size In sodoing we also show the profound affect that conti-nents have on the pattern of mantle convection

Properties of Mantle Convection

Five main properties of convection in the mantleare particularly relevant to this study (1) the exist-ence of cold rigid continental lithosphere underlainby a warm low-viscosity asthenosphere implies theexistence of a large viscosity contrast (gt3000 Pa-s)in the upper mantle (2) regular long-wavelengthconvection in the mantle in combination withhigh-intensity quasi-turbulent convection produceshot regions with varying shapes such as diapirssheets and ridges (3) the olivine-perovskite mantlephase transition at a depth of 660 km is endother-mic and results in partial stratification of convec-tion in the mantle (for example some subductedplates continue to descend into the lower mantlewhereas others remain above the phase transition)(4) mantle material at the typical P-T conditions ofoceanic lithosphere has a viscoplastic rheology thatproduces plate bending and the other mechanicalbehavior that we associate with plate tectonicsand (5) of particular importance to this study thepresence of continents above the convecting mantleprofoundly affects the form of that convection conti-nental ldquothermal blanketsrdquo lead to regular andpredictable patterns in the motions of both theconvection system and the continents

The first three properties were studied in greatdetail during the last three decades (eg see Schu-bert et al 2001) Taking into account the fourthproperty leads to convection models that self-con-sistently describe the breakup of oceanic lithos-phere into quasi-rigid plates (Tackley 2000a2000b Zhong et al 2000) This paper investigatesthe fifth property of mantle convection The effectsof floating continents on mantle convection areimportant on time scales of more than 200 mywhen continents behave like stable rigid bodiesespecially in comparison with the creation and sub-duction of oceanic lithospheric plates

Previous Convection ModelsIncorporating Moving Continents

The role of moving oceanic plates andor conti-nents in mantle convection has been modeled using

a numerical method that actually fixes mantle veloci-ties rather than independently describing plate veloc-ities (Olson and Corcos 1980 Davies 1986 19881989 Gurnis and Hager 1988 Gable et al 1991King et al 1992 Zhong and Gurnis 1995 Doin etal 1997) This approach can explain some aspects ofplate movement but could not be used to calculateplate velocities as an independent parameter

A method for the self-consistent calculation ofcontinental plate velocity within a convecting mantlewas proposed by Gurnis (Gurnis 1988 Gurnis andZhong 1991 Zhong and Gurnis 1993 1994) In thisapproach a continent is considered as a highlyviscous body floating in the mantle Gurnis (1988)calculated the velocity of continents in his 2-Dmodel by using a fixed marker point at the corner ofeach continent This provided the first quantitativedescription of the assembly and dispersal of two con-tinental blocks Additional studies were presentedby Gable et al (1991) Lowman and Jarvis (19931995 1996) Bobrov et al (1999) and Trubitsyn andRykov (1995 1998 2000) The latter authorsapproximated continents as rigid bodies (asdescribed by Eulerrsquos equations of motion) with vis-cous coupling to drive the plates (Trubitsyn 2000)An iterative procedure was used to model convec-tion taking into account the rotation of continentsand their mutual collisions Oceanic plates weredescribed by mantle convection equations incorpo-rating a visco-plastic rheology (Tackley 2000aZhong et al 2000) These studies showed that themantle under a fixed continent will become warmerand that eventually hot upwelling zones arise partic-ularly under large continents However it was shownby Gurnis (1988) Trubitsyn and Rykov (1998) andLowman and Jarvis (1996 1999)mdashand will bedemonstrated heremdashthat the motions of continentsproduce additional effects on mantle evolution

Input Parameters of Convection Models

Due to practical limitations on computationalresources it is not yet possible to make a numericalsimulation of mantle convection that exactlymatches the conditions in the real Earth Ourmodels do not match the real Earth in severalaspects (Table 1) First these models are two dimen-sional while real convection is three dimensionalSecond these models use basal heating onlywhereas both basal and internal heating drive realmantle convection Third our models use muchlower Rayleigh numbers than the Rayleigh number









TAB

LE 1

Inp

ut P

aram

eter

s fo

r C

onve

ctio

n M

odel

ing

Syst

emP

rese

nt E

arth

Supe

rcon

tine

ntSm

all c

onti

nent

App

endi

x

Ray

leig

h nu

mbe

r (R

a)1

00E

+07

500

E+

045

00E

+04

20E

6

Hea

ting

Bas

al +

inte

rnal

Bas

al o

nly

Bas

al o

nly

Bas

al +

inte

rnal

Vis

cosi

ty la

wP

ress

ure

tem

pera

ture

and

str

ess

depe

nden

t1

h =

h0e

xp[(ndash

46T

+ 0

92(

1 ndash

z)]

h =

h0e

xp[(ndash

46T

+ 0

92(

1 ndash

z)]

h =

h 0exp

[(ndash4

6T

+ 0

92(

1 ndash

z)]

Con

vect

ion

patte

rnT

hree

-dim

ensi

onal

Two-

dim

ensi

onal

Two-

dim

ensi

onal

Two-

dim

ensi

onal

Con

tinen

t dia

met

er k

mVa

riab

le30

0030

030

00

Sim

ulat

ion

dura

tion

my

38

0034

015

00

500

Pha

se b

ound

ary

at 6

60 k

mYe

sN

oN

oYe

s

Num

ber

of c

ells

Vari

able

105

Vari

able

1 See

for

exa

mpl

e F

orte

and

Mit

rovi

ca 2

000

Sch

uber

t et a

l 2

001

482 TRUBITSYN ET AL


















484 TRUBITSYN ET AL










486 TRUBITSYN ET AL














488 TRUBITSYN ET AL











Siberia 372E + 06 2175623

India 196E + 06 158094


Amazon 134E6 1306925






Arabia 397E + 06 2247


Eurasia 391E + 07 7052

India 431E + 06 2342

Africa 215E + 07 5233










Conclusions



490 TRUBITSYN ET AL







Acknowledgments


REFERENCES








































492 TRUBITSYN ET AL




























Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL
















TAB

LE 1

Inp

ut P

aram

eter

s fo

r C

onve

ctio

n M

odel

ing

Syst

emP

rese

nt E

arth

Supe

rcon

tine

ntSm

all c

onti

nent

App

endi

x

Ray

leig

h nu

mbe

r (R

a)1

00E

+07

500

E+

045

00E

+04

20E

6

Hea

ting

Bas

al +

inte

rnal

Bas

al o

nly

Bas

al o

nly

Bas

al +

inte

rnal

Vis

cosi

ty la

wP

ress

ure

tem

pera

ture

and

str

ess

depe

nden

t1

h =

h0e

xp[(ndash

46T

+ 0

92(

1 ndash

z)]

h =

h0e

xp[(ndash

46T

+ 0

92(

1 ndash

z)]

h =

h 0exp

[(ndash4

6T

+ 0

92(

1 ndash

z)]

Con

vect

ion

patte

rnT

hree

-dim

ensi

onal

Two-

dim

ensi

onal

Two-

dim

ensi

onal

Two-

dim

ensi

onal

Con

tinen

t dia

met

er k

mVa

riab

le30

0030

030

00

Sim

ulat

ion

dura

tion

my

38

0034

015

00

500

Pha

se b

ound

ary

at 6

60 k

mYe

sN

oN

oYe

s

Num

ber

of c

ells

Vari

able

105

Vari

able

1 See

for

exa

mpl

e F

orte

and

Mit

rovi

ca 2

000

Sch

uber

t et a

l 2

001

482 TRUBITSYN ET AL


















484 TRUBITSYN ET AL










486 TRUBITSYN ET AL














488 TRUBITSYN ET AL











Siberia 372E + 06 2175623

India 196E + 06 158094


Amazon 134E6 1306925






Arabia 397E + 06 2247


Eurasia 391E + 07 7052

India 431E + 06 2342

Africa 215E + 07 5233










Conclusions



490 TRUBITSYN ET AL







Acknowledgments


REFERENCES








































492 TRUBITSYN ET AL




























Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL








482 TRUBITSYN ET AL


















484 TRUBITSYN ET AL










486 TRUBITSYN ET AL














488 TRUBITSYN ET AL











Siberia 372E + 06 2175623

India 196E + 06 158094


Amazon 134E6 1306925






Arabia 397E + 06 2247


Eurasia 391E + 07 7052

India 431E + 06 2342

Africa 215E + 07 5233










Conclusions



490 TRUBITSYN ET AL







Acknowledgments


REFERENCES








































492 TRUBITSYN ET AL




























Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL












484 TRUBITSYN ET AL










486 TRUBITSYN ET AL














488 TRUBITSYN ET AL











Siberia 372E + 06 2175623

India 196E + 06 158094


Amazon 134E6 1306925






Arabia 397E + 06 2247


Eurasia 391E + 07 7052

India 431E + 06 2342

Africa 215E + 07 5233










Conclusions



490 TRUBITSYN ET AL







Acknowledgments


REFERENCES








































492 TRUBITSYN ET AL




























Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL













486 TRUBITSYN ET AL














488 TRUBITSYN ET AL











Siberia 372E + 06 2175623

India 196E + 06 158094


Amazon 134E6 1306925






Arabia 397E + 06 2247


Eurasia 391E + 07 7052

India 431E + 06 2342

Africa 215E + 07 5233










Conclusions



490 TRUBITSYN ET AL







Acknowledgments


REFERENCES








































492 TRUBITSYN ET AL




























Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL












488 TRUBITSYN ET AL











Siberia 372E + 06 2175623

India 196E + 06 158094


Amazon 134E6 1306925






Arabia 397E + 06 2247


Eurasia 391E + 07 7052

India 431E + 06 2342

Africa 215E + 07 5233










Conclusions



490 TRUBITSYN ET AL







Acknowledgments


REFERENCES








































492 TRUBITSYN ET AL




























Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL















Conclusions



490 TRUBITSYN ET AL







Acknowledgments


REFERENCES








































492 TRUBITSYN ET AL




























Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL








490 TRUBITSYN ET AL







Acknowledgments


REFERENCES








































492 TRUBITSYN ET AL




























Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL








































492 TRUBITSYN ET AL




























Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL









Appendix A


















(5)


dx1 dt = u0 (6)


mparau0 parat





+[ ] xd

x1

x2

ograve

ndashd

1ndash d

1

ograve

ndashd

1ndash d

1

ograve

=

494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL








494 TRUBITSYN ET AL





Boundary conditions


(8)











Appendix B





1 dndash

1

ograve


xd

x1

x1 l+

ograve

+

0=





496 TRUBITSYN ET AL












496 TRUBITSYN ET AL








cold cratonic roots and thermal blankets: how continents ......was proposed by gurnis (gurnis, 1988;...

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